Q is INTEGER
The number of columns in X11 and X21. 0 <= Q <= M and
M-Q <= min(P,M-P,Q).

X11

X11 is COMPLEX array, dimension (LDX11,Q)
On entry, the top block of the matrix X to be reduced. On
exit, the columns of tril(X11) specify reflectors for P1 and
the rows of triu(X11,1) specify reflectors for Q1.

LDX11

LDX11 is INTEGER
The leading dimension of X11. LDX11 >= P.

X21

X21 is COMPLEX array, dimension (LDX21,Q)
On entry, the bottom block of the matrix X to be reduced. On
exit, the columns of tril(X21) specify reflectors for P2.

LDX21

LDX21 is INTEGER
The leading dimension of X21. LDX21 >= M-P.

THETA

THETA is REAL array, dimension (Q)
The entries of the bidiagonal blocks B11, B21 are defined by
THETA and PHI. See Further Details.

PHI

PHI is REAL array, dimension (Q-1)
The entries of the bidiagonal blocks B11, B21 are defined by
THETA and PHI. See Further Details.

TAUP1

TAUP1 is COMPLEX array, dimension (P)
The scalar factors of the elementary reflectors that define
P1.

TAUP2

TAUP2 is COMPLEX array, dimension (M-P)
The scalar factors of the elementary reflectors that define
P2.

TAUQ1

TAUQ1 is COMPLEX array, dimension (Q)
The scalar factors of the elementary reflectors that define
Q1.

PHANTOM

PHANTOM is COMPLEX array, dimension (M)
The routine computes an M-by-1 column vector Y that is
orthogonal to the columns of [ X11; X21 ]. PHANTOM(1:P) and
PHANTOM(P+1:M) contain Householder vectors for Y(1:P) and
Y(P+1:M), respectively.

WORK

WORK is COMPLEX array, dimension (LWORK)

LWORK

LWORK is INTEGER
The dimension of the array WORK. LWORK >= M-Q.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

The upper-bidiagonal blocks B11, B21 are represented implicitly by angles THETA(1), ..., THETA(Q) and PHI(1), ..., PHI(Q-1). Every entry in each bidiagonal band is a product of a sine or cosine of a THETA with a sine or cosine of a PHI. See [1] or CUNCSD for details.

P1, P2, and Q1 are represented as products of elementary reflectors. See CUNCSD2BY1 for details on generating P1, P2, and Q1 using CUNGQR and CUNGLQ.